Non-Collinear and Non-Coplanar Magnetic Orders in 1/1 Periodic Approximant to the Icosahedral Quasicrystal

Abstract

Ground-state properties of rare-earth based 1/1 periodic approximants of icosahedral quasicrystal are clarified theoretically on the basis of an effective model for magnetism taking into account uniaxial anisotropy arising from crystalline electric field. By performing numerically-exact calculation on the 1/1 approximant crystal with a lattice constant $a$=14.725 Å, we have determined the ground-state phase diagram for ferromagnetic interactions. The result shows that eight kinds of noncollinear and noncoplanar magnetic structures are stabilized, whose magnetic space groups are identified as $I_{\mathrm{P}}{m}^{\prime }{\bar{3}}^{\prime }$, $C{2}^{\prime }/m^{\prime }$ and $R\bar{3}$. We have clarified the degeneracy of each ground state, which is expected to be reflected in the numbers of the domains. By analyzing each state, the magnetic as well as topological properties are revealed. Our results are shown to explain the measured magnetic structures in the 1/1 approximants and the effective model is discussed to be useful for understanding the magnetic structures and their topological properties in broad range of rare-earth based 1/1 approximants.

15 pages, 19 figures, Selected as JPSJ Editor's Choice, Selected as JPS Hot Topics

References in corpus (16)

• Antiferromagnetic order in the Hubbard Model on the Penrose Lattice
• Noncoplanar ferrimagnetism and local crystalline-electric-field anisotropy in the quasicrystal approximant Au${}_{70}$Si${}_{17}$Tb${}_{13}$
• Superlattice structure in the antiferromagnetically ordered state in the Hubbard model on the Ammann-Beenker tiling
• Hedgehog-lattice spin texture in classical Heisenberg antiferromagnets on the breathing pyrochlore lattice
• Magnetic orders induced by RKKY interaction in Tsai-type quasicrystalline approximant Au-Al-Gd
• Topological magnetic textures and long-range orders in Tb-based quasicrystal and approximant
• Magnetism and topology in Tb-based icosahedral quasicrystal
• Ferrimagnetically ordered states in the Hubbard model on the hexagonal golden-mean tiling
• Effect of Electron-Electron Interactions on Metallic State in Quasicrystals
• Classical and Quantum Magnetic Ground States on an Icosahedral Cluster
• Crystalline Electronic Field in Rare-Earth Based Quasicrystal and Approximant: Analysis of Quantum Critical Au-Al-Yb Quasicrystal and Approximant
• Revisit of magnetic orders in 1/1 approximant crystals of Tsai-type quasicrystal from theoretical points of view
• Monte Carlo study on critical exponents of the classical Heisenberg model in ferromagnetic icosahedral quasicrystal
• Crystalline Electronic Field and Magnetic Anisotropy in Dy-based Icosahedral Quasicrystal and Approximant
• Short-range magnetic correlations in quasicrystalline i-Tb-Cd
• Identification of Two Distinct Antiferromagnetic Phases in the Au-Al-Gd Quasicrystal Approximant